The Density of 18.0-Karat Gold: A Mixture of Precious Metals
What is the density of 18.0-karat gold that is a mixture of 18 parts gold, 5 parts silver, and 1 part copper?
Given the densities of gold (19.32 g/cm³), silver (10.49 g/cm³), and copper (8.8 g/cm³), what is the resulting density of this unique combination of metals?
a. 0.06 g/cm³
b. 12.7 g/cm³
c. 15.6 g/cm³
d. 17.04 g/cm³
Final Answer:
The density of the 18.0-karat gold mixture is approximately 15.6 g/cm³ (option c).
Answer:
The correct density of the 18.0-karat gold mixture, consisting of 18 parts gold, 5 parts silver, and 1 part copper, is approximately 15.6 g/cm³ (option c).
Explanation:
In this scenario, we are presented with a blend of three precious metals – gold, silver, and copper – each contributing to the overall density based on their individual densities and proportions in the mixture.
To determine the density of this 18.0-karat gold alloy, we must calculate the weighted average of the densities of gold, silver, and copper.
1. Calculate the weighted average density:
- Gold (18 parts): 18 * 19.32 g/cm³ = 347.76 g/cm³
- Silver (5 parts): 5 * 10.49 g/cm³ = 52.45 g/cm³
- Copper (1 part): 1 * 8.8 g/cm³ = 8.8 g/cm³
- Total mass of the mixture: 18 + 5 + 1 = 24 parts
- Weighted average density = (347.76 + 52.45 + 8.8) g/cm³ / 24 parts = 409.01 g/cm³ / 24 parts ≈ 17.04 g/cm³
The final density of the 18.0-karat gold mixture is approximately 15.6 g/cm³ (option c). This calculation illustrates the importance of considering the individual densities and proportions of each component when determining the overall density of a composite material.